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Question: 4 voluntary contribution to public goods free riding and crowding...

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4. Voluntary Contribution to Public Goods, Free Riding, and Crowding Out Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all of life in the city. There are only two residents willing to live within city-limits, Abe and Betty. Abes income is Ya-460, and Bettys income is YB-440. A traveling salesman is visiting the town, offering odor conversion units, which conveniently input garlic odor and output clean air. Abe and Betty have the same preference (utility function) over clean air (C) and all private consumption goods (ri): U-5In(r)+In(C), ie A, B) The total provision of clear air is given as the sum of individual purchases: C = CA + CB. The price of clean air is 2 while the price of all private goods is 1 (a) Calculate each individuals private provision of clean air, taking the others provision as given. That is, solve for Ca as a function of CB in Abes optimization problem, and solve for CB as a function of Ca in Bettys optimization problem. Can you explain the sign on the other residents contribution in these response functions? (b) If the government does not intervene, what level of clean air will be provided? How many units are provided by Abe? How many by Betty? (c) What is the socially optimal level of clean air provision? (Use a utilitarian social welfare function.) Does this value differ from that found in (b)? Explain in the context of externalities

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